Question

the figure below is a square. find the length of side ( x ) in simplest radical form with a rational denominator.

Explanation:

Step1: Apply Pythagorean theorem

For a square, the diagonal $x$ relates to side length $\sqrt{3}$ by $x^2 = (\sqrt{3})^2 + (\sqrt{3})^2$

Step2: Calculate squared terms

$(\sqrt{3})^2 = 3$, so $x^2 = 3 + 3 = 6$

Step3: Solve for x, rationalize if needed

$x = \sqrt{6}$ (already simplified, denominator is rational)

Answer:

$\sqrt{6}$